Multiple Choice
In simple linear regression (as in Excel’s trendline output), the model is written as . What do and represent?
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12. Regression
Regression Line Equation and Coefficient of Determination - Excel
Multiple Choice
In the regression line equation (as used in Excel trendlines), what does represent?
A
The y-intercept: the predicted value of when
B
The coefficient of determination , the proportion of variation in explained by
C
The correlation coefficient between and
D
The slope: the change in predicted for a one-unit increase in
Verified step by step guidance1
Recall the general form of the regression line equation: \(y = m x + b\), where \(y\) is the predicted value, \(x\) is the independent variable, \(m\) is the slope, and \(b\) is the y-intercept.
Understand that the y-intercept \(b\) represents the predicted value of \(y\) when \(x = 0\). This means it is the point where the regression line crosses the y-axis.
Recognize that the slope \(m\) indicates how much \(y\) changes for a one-unit increase in \(x\), but this is different from the y-intercept \(b\).
Note that the coefficient of determination \(R^2\) measures the proportion of variation in \(y\) explained by \(x\), and the correlation coefficient \(r\) measures the strength and direction of the linear relationship between \(x\) and \(y\); neither of these are represented by \(b\).
Therefore, \(b\) specifically corresponds to the y-intercept, the predicted value of \(y\) when \(x\) equals zero.
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